1.

Find the general solutions of equation `sin^(4)x + cos^(4)x=sinx cosx`

Answer» Using half-angle formulae, we can represent given equation in the form:
`rArr ((1-cos2x)/2)^(2)+((1+cos2x)/2)^(2) = sinx cosx`
`rArr (1-cos2x)^(2) + (1+cos2x)^(2)=4sinx cosx`
`rArr sin^(2)2x +sin2x = 2`
`rArr sin2x = 1` or `sin2x =-2` (which is not possible)
`2x=2npi+pi/2, n in I`
`rArr x=npi + pi/4, n in I`


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